Summary: Extensional Normalization in the Logical Framework with
Proof Irrelevant Equality
Andreas Abel
Department of Computer Science
Ludwig-Maximilians-University Munich
Abstract
We extend the Logical Framework by proof irrelevant
equality types and present an algorithm that computes
unique long normal forms. The algorithm is inspired by
normalization-by-evaluation. Equality proofs which are not
reflexivity are erased to a single object . The algorithm
decides judgmental equality, its completeness is established
by a PER model.
1. Introduction
In intensional Martin-L®of type theory (ITT), but also
in the Calculus of Inductive Constructions which underlies
the Coq proof assistant, we distinguish between definitional
equality of terms t and t of type T, given by the judgement
t = t : T, and propositional equality which is estab-
lished by providing an inhabitant of the identity set IdT t t .